Details

Time bar (total: 12.8s)

sample48.0ms

Algorithm
intervals
Results
10.0ms188×body80valid
7.0ms20×body320valid
6.0ms26×body640valid
5.0ms256×pre80true
4.0ms14×body1280valid
1.0ms8×body160valid

simplify51.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite923.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
207.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
640.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
72.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series655.0ms

Counts
3 → 9
Calls
3 calls:
255.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
310.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
90.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify98.0ms

Counts
120 → 120

prune365.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.4b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite805.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
205.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
51.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
414.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
115.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series827.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
254.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
307.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify74.0ms

Counts
307 → 307

prune853.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.4b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
152×*-un-lft-identity
117×add-sqr-sqrt
90×associate-*r*
76×add-cube-cbrt
22×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×add-exp-log add-cbrt-cube
12×cbrt-prod associate-/r/
10×flip3-+ flip-+
6×pow1 div-inv add-log-exp
5×associate-/l*
4×cbrt-undiv div-exp associate-*l*
3×unpow-prod-down cube-prod prod-exp associate-/r* cbrt-unprod unswap-sqr
2×cube-div frac-times cbrt-div associate-*l/ associate-/l/
1×+-commutative cube-mult flip3-- frac-2neg pow1/3 unpow3 div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-- rem-cbrt-cube sqr-pow
Counts
4 → 191
Calls
4 calls:
213.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
51.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
411.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
115.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series994.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
85.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
264.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
326.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify51.0ms

Counts
203 → 203

prune689.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.4b
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.3b
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
39×add-cbrt-cube
28×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
13×*-un-lft-identity
9×pow1 frac-times
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt flip3-+ flip-+
6×associate-*r/ add-log-exp
5×associate-*l/
4×cbrt-div associate-*l*
3×pow-prod-down distribute-lft-out
2×pow1/3
1×+-commutative associate-*r* sum-log *-commutative
Counts
4 → 91
Calls
4 calls:
67.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
67.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
933.0ms
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
909.0ms
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series987.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
196.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
321.0ms
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify102.0ms

Counts
103 → 103

prune339.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.6b

regimes287.0ms

Accuracy

11.1% (6.0b remaining)

Error of 12.0b against oracle of 6.0b and baseline of 12.8b

bsearch61.0ms

Steps
ItersRangePoint
6
6.4496730188069095e+94
2.8646543636906463e+95
2.820006962648861e+95

simplify1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
718.0ms6311×body80valid
241.0ms8000×pre80true
237.0ms520×body1280valid
121.0ms587×body640valid
57.0ms381×body320valid
20.0ms201×body160valid